1 Downscaling of SMAP soil moisture using land surface temperature 1 and vegetation data 2 3 4 5 6 Bin Fang and Venkataraman Lakshmi 7 School of Earth Ocean and Environment, University of South Carolina Columbia 8 SC 29208 USA 9 Corresponding author [email protected]10 Rajat Bindlish 11 Hydrological Sciences Branch, NASA Goddard Space Flight Center Greenbelt MD 12 20771 USA 13 Thomas J Jackson 14 Hydrology and Remote Sensing Laboratory, Beltsville Agricultural Research 15 Center, USDA-ARS Beltsville MD 20705 16 17 18 19 20 21 https://ntrs.nasa.gov/search.jsp?R=20180004874 2020-08-01T07:38:44+00:00Z
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Downscaling of SMAP soil moisture using land surface … · 2019-09-20 · 2 1 . ABSTRACT 2 Remotely sensed soil moisture retrieved by the Soil Moisture Active and Passive (SMAP)
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1
Downscaling of SMAP soil moisture using land surface temperature 1
and vegetation data 2
3
4
5
6
Bin Fang and Venkataraman Lakshmi 7
School of Earth Ocean and Environment, University of South Carolina Columbia 8
Where, 𝜃𝜃(𝑠𝑠, 𝑡𝑡) stands for a 1 km bias corrected SMAP soil moisture at the MODIS grid 15
(𝑠𝑠, 𝑡𝑡). 𝛩𝛩 is the 9 km SMAP soil moisture in the morning overpass. 𝜃𝜃�𝑁𝑁 are the N of uncorrected 1 16
km SMAP soil moisture grids that fall in the 9 km SMAP grid 𝛩𝛩. 17
The downscaled soil moisture has the following characteristics: (a) the soil moisture at 1 18
km can be computed by the relationship between soil moisture and daily temperature variation, 19
(b) the bias between SMAP and MODIS derived soil moisture can be eliminated at the low 20
resolution, and (c) the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship varies in response to different vegetation conditions. 21
3.2 Data Processing 22
13
The Inverse Distance Weighting (IDW) method was applied for upscaling of LTDR and 1
PALS data. It is a nonlinear interpolation technique using the weighted average of the values 2
surrounding the predicted location. The IDW method assumes the influence of each measured 3
point reduces as the distance increases, hence the weight becomes smaller. For any grid 𝑍𝑍𝑙𝑙𝑙𝑙 at 4
low spatial resolution to be upscaled from high resolution grids 𝑍𝑍ℎ𝑖𝑖, it can be computed by using 5
𝑍𝑍𝑙𝑙𝑙𝑙 =∑ 𝑍𝑍𝑛𝑛
ℎ𝑖𝑖
𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙𝑛𝑛
∑ 1𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙
𝑛𝑛 (3) 6
The n of high spatial resolution neighbor grids 𝑍𝑍ℎ𝑖𝑖 were used to generate the new grid at 7
low spatial resolution 𝑍𝑍𝑙𝑙𝑙𝑙. n is determined by the number of 𝑍𝑍ℎ𝑖𝑖 grids that fall in the 𝑍𝑍𝑙𝑙𝑙𝑙. 𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙 is 8
the distance between the centroids of 𝑍𝑍ℎ𝑖𝑖 and 𝑍𝑍𝑙𝑙𝑙𝑙. 9
In a few occasions, the 1 km grid may overlap with more than one 12.5 km grid (2~4 10
adjacent grids at most) so multiple modeled 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship equations from the overlapped 11
12.5 km grids should be applied on the 1 km MODIS LST for calculating soil moisture. We 12
applied an averaging method based on the proportion of each overlapped NLDAS grid to solve 13
this issue. 14
𝜃𝜃�′ = 1𝑛𝑛∑ 𝑃𝑃𝑛𝑛 ∗ 𝜃𝜃�𝑛𝑛′ (4) 15
Where, 𝜃𝜃�′ is the adjusted uncorrected 1 km soil moisture, n is the number of 12.5 km 16
grids overlapped the 1 km grid. 𝑃𝑃 is the proportion in percentage of each 12.5 km grid 17
overlapped the 1 km grid, and 𝜃𝜃�𝑛𝑛′ is the soil moisture value calculated by each 12.5 km grid 18
corresponded 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship equation. 19
20
3.3 Validation 21
14
The original and downscaled SMAP soil moisture data were evaluated using in situ soil 1
moisture observations acquired from SMAPVEX15 campaign, which are point estimates at the 2
permanent and temporary network stations, as well as the upscaled PALS soil moisture retrievals 3
at 1 km and 9 km resolutions. The in situ soil moisture measurements that fall in each 1 km/ 9 4
km soil moisture grid were averaged for comparison. The statistical variables include R2, slope, 5
unbiased RMSE, bias and p-value from significance test of Pearson correlation coefficient. In 6
order to compare the three estimated soil moisture products: 1 km / 9 km SMAP soil moisture 7
and PALS soil moisture through the sampling days in SMAPVEX15, results were analyzed using 8
the histogram plots showing distribution form, Empirical Cumulative Distribution Function 9
(ECDF) plots as well as time series plots showing mean and standard deviation. 10
11
4.0 RESULTS AND DISCUSSION 12
4.1 𝜽𝜽 - ∆𝑻𝑻𝒔𝒔 relationship 13
NLDAS data from 1981-2016 were used to estimate the model function between 𝜃𝜃 and ∆𝑇𝑇𝑠𝑠 14
which is modulated by NDVI. Three NLDAS grids were selected to demonstrate the relationships 15
for the three SMAPVEX15 study sites: Walnut Gulch, Empire Ranch and Santa Rita. From Table 16
1, the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 regression fit lines are negatively correlated for all three sites. Walnut Gulch has 17
better R2 (0.5 - 0.809) than the other two sites. The R2 do not vary much as NDVI increases. From 18
the Figure 3, the ranges of slope for the three sites are -106.127 to -66.565, -66.239 to -47.302, 19
-79.861 to -66.478, respectively. The ranges of slope for Walnut Gulch and Santa Rita are smaller 20
than for Empire Ranch. The NDVI-based classes differentiate the data pairs and the five regression 21
fit lines line up well from top to bottom which correspond to the NDVI classes from the highest to 22
the lowest. From the scatterplot, given any ∆𝑇𝑇𝑠𝑠 value, the soil moisture corresponding to the 23
15
highest NDVI class (>0.4) are approximately 0.1 m3/m3 wetter than the lowest class (NDVI<0.1). 1
The results show that the NDVI - 𝑇𝑇𝑠𝑠 triangle principle is applicable in this study domain and can 2
be used to downscale the SMAP soil moisture estimates. With regard to the significance of the 3
correlations between 𝜃𝜃 and ∆𝑇𝑇𝑠𝑠 , the results show that the p-values of the correlations of all NDVI 4
classes from all three sites are much smaller than a significance level of 0.01. 5
4.2 1 km downscaled soil moisture 6
Figure 4 shows the soil moisture maps for the 1 km downscaled, the SMAP 9 km and the 7
SMAP 36 km products 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃36𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , as well as difference between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 8
𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 respectively for the five sampling days (8th, 10th, 13th, 16th, 18th of August, 2015). It can be 9
seen that the soil moisture distribution pattern was consistent between the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 10
the original product 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, while the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 displayed greater spatial variability. However, if we 11
compare the difference between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 through all five days, we find that the 12
distribution patterns of the two products exhibited discrepancies, especially in central and 13
southeast Arizona where the soil moisture pattern was more complex. In these regions, 𝜃𝜃36𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 did 14
not show any wetting or dry-down zones, which were found in the two finer resolution estimates. 15
The 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 images demonstrated greater spatial heterogeneity of soil moisture over the 16
SMAPVEX15 domain. The 500 m resolution PALS L-band radiometer soil moisture was retrieved 17
using a version of the SMAP baseline algorithm (Single Channel Algorithm-Vertical Polarization) 18
(Jackson et al., 1993, 2010) and upscaled to 1 km in order to compare directly with the 1km 19
downscaled SMAP soil moisture. Figure 5 shows that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 compares well with the upscaled 20
1 km PALS soil moisture 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 and SMAP 9 km soil moisture 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 for the five sampling days. 21
The black grids over each map outline the 9 km grid boundaries for easier visualization of the 22
downscaled soil moisture heterogeneity within the coarser resolution grid. It can be summarized 23
16
that within each 9 km grid, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 displayed soil moisture features in more detail than the 1
original 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, as well as similar spatial distribution pattern with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. For instance, the spatial 2
heterogeneity was more visible near the boundaries between the San Pedro River basin and Santa 3
Cruz River Basin and Whitewater Draw Basin. However, the overall range of soil moisture values 4
for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 was generally lower than that of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 . When compared for each day, the 5
discrepancies between the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 could be noted in Figure 5. Looking at the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 6
product, two dry zones in middle west and east were apparent on August 8, as well as a wet zone 7
with a belt shape on August 16 which were not observed in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆maps. Some small and isolated 8
spots showed stronger drying or wetting trends than surrounding areas in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆, which were not 9
present in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. Additionally, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 showed greater contrast between the highest and lowest 10
soil moisture values than 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 . As opposed to this, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 showed better 11
consistency on the other two days August 10 and 18. 12
The comparisons between uncorrected 1 km soil moisture 𝜃𝜃�1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 calculated from 13
downscaling model and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are shown in Figure 6. Better correlations were found in August 14
16 and 18, with unbiased RMSE (µbRMSE) = 0.026 and 0.019, bias = 0.03 and 0.025, respectively. 15
More scattered characteristic was noted especially on August 8, which had µbRMSE of 0.043 and 16
bias of 0.048. Such inconsistency between 𝜃𝜃�1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might have influences on the 17
downscaled soil moisture. 18
Figure 7 shows the frequency distribution histogram of the three soil moisture products. It 19
can be summarized that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 had more similar shape and data ranges as 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 than 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, 20
which had skewed or bimodal shapes on August 10, 13 and 16 and narrower ranges of the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 21
for corresponding days. Additionally, more similar data ranges and shapes of soil moisture values 22
17
between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 were observed in August 13 and 18, while 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had narrower ranges 1
than 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 for the other three days. 2
The ECDF curves for the three soil moisture products 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 for the five 3
SMAPVEX15 sampling days of descending overpasses are displayed in Figure 8. It was found 4
that the ECDF curves of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had better agreement with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 than 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , which might 5
indicate the improved accuracy of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. However, the inconsistency between PALS and SMAP 6
was noted from three days: August 8, 10 and 16, of which 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had limited improvement of 7
𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. 8
The overall mean and standard deviation values of the three soil moisture products as well 9
as the in situ measurements are shown as a time series in Figure 9. From the top graph, it can be 10
observed that the mean values of in situ were always drier than the other three data sets, whereas 11
the mean values of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 were closer to either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ than the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. In addition, 12
August 13, 16, and 18 were found to have better agreement among the four data sets than August 13
8 and 10. Examining the bottom graph, the standard deviations of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 were 14
approximately 0.02 m3/m3 lower than either the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ. The 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 was more consistent 15
with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 on August 13 and 18, while it was more consistent with in situ observations 16
for the other three days. 17
4.3 Validation 18
Table 2 and Figure 10 shows the results of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validated using 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. 19
The following observations can be made based on the validation results in Table 1: (1) the R2 of 20
the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are higher and they range 0.189 – 0.697 for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and ranges 0.003 - 0.597 for the 21
𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, (2) the slopes for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are slightly higher for August 8, 10 and 18. They range 0.518 22
- 1.552 for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and range 0.07 - 1.915 for the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, (3) the µbRMSEs and the biases are 23
18
improved on four days for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 over the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, ranging 0.009 - 0.02 m3/m3 and -0.002 - 1
0.01 m3/m3, respectively. The range of µbRMSEs for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 meets the criteria that RMSE < 2
0.04 m3/m3 for validated SMAP soil moisture estimates. Additionally, the p-values of the Pearson’s 3
correlation coefficient for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are all much smaller than the significance level 𝛼𝛼 = 0.05, 4
indicating significant correlations between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. Examining the scatterplots in Figure 5
10, it appears that the locations of the highest density data points in the 1 km plots correspond to 6
the locations of points in 9 km plots. From this figure, it is also seen that there is a relatively better 7
consistency between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 . However, it should be noted that there is an obvious 8
underestimation trend for either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 or 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 when comparing to the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. In addition, it is 9
observed that the PALS soil moisture values cover a wider range (approximately 0.05 - 0.25 m3/m3) 10
than either the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(approximately 0.1 - 0.2 m3/m3), which probably indicates greater 11
soil moisture spatial variability. This fact corresponds to what is observed in Figure 5, 7 and 9. 12
Table 3 and Figure 11 illustrates the validation results for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 using the in 13
situ measurements. In this validation, only the 9 km 𝜃𝜃 grids having more than 8 in situ points 14
within their boundaries were considered. For the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, the R2 range 0.255 - 0.733 and µbRMSEs 15
range 0.006 - 0.044 m3/m3, comparing with the R2 range of < 0.001 - 0.353 and µbRMSEs range 16
of 0.03 - 0.088 m3/m3 for validation results of 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 . It can be concluded that the validation 17
metrics of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 show an obvious improvement over 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and the RMSE range of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 18
meets the criteria < 0.04 m3/m3 for SMAP soil moisture. The improvement may also be observed 19
in the slope values as well as the plots shown in Figure 11, where the scatter points for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are 20
closer to the 1-1 diagonal line. The p-values for the Pearson’s correlation coefficient for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 21
are significant at the 𝛼𝛼 = 0.05 significance level. Additionally, the bias range of -0.029 - < 0.001 22
m3/m3 for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 also indicates the underestimation tendency as compared to the in situ data. 23
19
The downscaling algorithm had varying performance on different days. One explanation 1
could be that the precipitation during SMAPVEX15 may have an impact on the performance of 2
the downscaling algorithm. As Figure 2 shows, it rained more between August 7 and 12 than after 3
August 13, which corresponded to the relatively higher µbRMSE for August 8, 10 and 13 and 4
validation results using in situ data in Figure 11. Additionally, the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might not 5
be sensitive to the wetting trends in the central and southern regions (August 8 and 10 in Figure 6
5). Similarly, another inconsistency was noted in the regions showing very dry condition in the 7
eastern part of SMAPVEX15 for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 in August 8, 10 and 16. However, these features were not 8
fully captured in these regions for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. In addition, the spatial heterogeneity between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 9
and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 observed for the day with less amount of rain (August 18) had better agreement than 10
the other days. Secondly, the bias of 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might also influence the downscaling model 11
performance, as the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 was corrected by 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. So, if the original SMAP soil 12
moisture is biased, the uncertainties will be passed down to the downscaled product. 13
There is a contradictory issue that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validation of August 18 had the worst R2 14
but the best µbRMSE. One possible explanation could be 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validation of this day had 15
narrower data range and lower variance than the other days. Additionally, better validation 16
metrics: R2 and µbRMSE for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 using in situ data were shown for August 18 than for other 17
days in Figure 11 and Table 3 and therefore we are confident that the algorithm still performs 18
well for August 18. 19
The PALS soil moisture was retrieved from the high spatial resolution L-band TB provided 20
by the aircraft system using the SCA (Single Chanel Algorithm), which calculated soil moisture 21
from single wavelength (L-Band) radiometer observations as well as other ancillary data such as 22
soil properties, comparing with the 1 km downscaled SMAP soil moisture estimated from multiple 23
20
spaceborne observations (visible/infrared spectroradiometer derived LST and NDVI products as 1
well as coarse resolution microwave radiometer derived soil moisture). The uncertainties in the 2
soil moisture retrieval algorithm likely contributed to weaker results for the SMAP downscaled 3
soil moisture estimates than the PALS retrievals. 4
This investigation introduced several improvements to the soil moisture downscaling 5
algorithm proposed by Fang et al. (2013). First, the original algorithm used only three NDVI 6
classes for building the NDVI corresponded 𝜃𝜃-∆𝑇𝑇𝑠𝑠 model. The revised algorithm divides this into 7
5 classes with the increment of 0.1, which better characterizes the NDVI modulated 𝜃𝜃-∆𝑇𝑇𝑠𝑠 8
relationship. Second, the original algorithm used the “drop-in-bucket” method for upscaling data 9
to coarser resolution, while the revised algorithm applies an IDW interpolation technique that 10
considers the distance between the new and fine resolution grid. And third, we applied an 11
averaging method to improve the accuracy of the calculated 1 km soil moisture grids which 12
overlap multiple 12.5 km (NLDAS) grids. Finally, we are now computing the downscaled soil 13
moisture corresponding to the SMAP descending 6:00am overpass rather than calculating a daily 14
averaged soil moisture. 15
Fang et al. (2013) point out that there were four limitations mentioned in the original 16
downscaling algorithm. We have attempted to overcome these limitations in the current 17
investigation. First, it is often very difficult to recover the cloud-contaminated pixels and the 18
current cloud-remover algorithms may cause uncertainties. In this study, we selected MODIS 19
data for the sampling days of SMAPVEX15 campaign site (it rarely rained during the latter part 20
of the campaign) for testing the downscaling algorithm. Second, the downscaling model was 21
built using 5 km AVHRR NDVI data, while the model was applied on 1 km MODIS NDVI data. 22
The AVHRR NDVI and MODIS NDVI data of overlapping period (since 2001) are at different 23
21
spatial resolutions. Third, this article is a new application (our past application has been in 1
Oklahoma) of the improved soil moisture downscaling algorithm by Fang et al. (2013). The 2
validation results for downscaled soil moisture indicate the improvement of accuracy over the 3
downscaled AMSR-E soil moisture in Fang et al. (2013) paper. Additionally, we also worked to 4
improve the downscaling model performance, using IDW technique. Finally, as mentioned 5
above, the other soil moisture related variables are often difficult to acquire. For example, the 6
related variables, including soil properties, topography and land cover information can be 7
acquired at very small scale of regions, which cannot fulfill the demands of providing soil 8
moisture estimates of wider range. So, we need to use the simplified downscaling model based 9
on the thermal inertia theory between temperature difference, soil moisture and vegetation. 10
Cosh et al. (2004) noted several inconsistency issues between the downscaled remotely 11
sensed soil moisture and in situ observations. First, the remote sensing data sets provide the soil 12
moisture data for an ellipsoidal region at a kilometer scale, as opposed to the in situ ground 13
observations that record the soil moisture at the point scale. There are also potential mismatches 14
in the sensing depth among all the soil moisture data sets. The brightness temperatures sensed by 15
the passive microwave sensor (SMAP) and MODIS, soil moisture output from NLDAS, as well 16
as the soil moisture measured by the SMAPVEX15 stations are all at different depths. The 17
passive microwave sensors typically penetrate a few centimeters, while the MODIS penetrates 18
only a few of millimeters, which are then compared with the NLDAS output soil moisture at 0-19
10 cm depth and the SMAPVEX15 ground measurements at 5 cm depth. Based on a previous 20
study, the satellite-based soil moisture is expected to be noisier than LSM data (Fang et al., 21
2016). The actual contributing domain used to compute the SMAP L3 soil moisture product is at 22
33 km rather than 9 km. So, the discrepancy between assumed or grid resolution and actual 23
22
resolution could be a source of error, especially in the regions of strong heterogeneity. Due to a 1
lack of a long-term monitoring of very high spatial resolution of land surface variables, the 2
NLDAS outputs as well as AVHRR and MODIS products were upscaled to 12.5 km for 3
downscaling the microwave soil moisture to 1 km. The spatial heterogeneity at 1 km within each 4
12.5 km grid during the model implementation was also ignored. 5
6
5.0 CONCLUSIONS 7
This study implemented a soil moisture downscaling algorithm with the SMAP Level 3 8
Radiometer Enhanced 9 km daily soil moisture product and validated the results using airborne 9
PALS radiometer and in situ soil moisture measurements from the SMAPVEX15 field campaign 10
in Arizona. This algorithm was developed based on a vegetation modulated daytime soil 11
moisture - daily surface temperature change relationship. The algorithm uses only three 12
variables: surface temperature, soil moisture and NDVI, as it is usually difficult to obtain high 13
spatial resolution data for other soil moisture related variables, such as precipitation, soil 14
properties and ET. The modeled relationship was applied on 1 km MODIS Aqua/Terra LST data 15
to compute 1 km soil moisture, which was then bias corrected by SMAP 9 km soil moisture. 16
Data from the five sampling days with aircraft coverage during the SMAPVEX15 campaign 17
were used for soil moisture and validation along with in situ data sets. It was found that soil 18
moisture spatial variability as well as dry-down and wetting trends were better characterized by 19
the downscaled estimates than the original 9 km SMAP estimates. The 1 km downscaled and 9 20
km SMAP soil moisture estimates were validated using the SMAPVEX15 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 retrievals and 21
the in situ measurements. The validation metrics of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 showed overall better consistency 22
with the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 than the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, with R2 increased by 0.169, µbRMSE decreased by 0.002 m3/m3 23
23
and bias decreased by 0.004 m3/m3. The downscaled soil moisture estimates also compared well 1
with the in situ soil moisture over the SMAPVEX15 study domain. The validation metrics for 2
𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 has the following improvements on 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆: R2 improved by 0.293, µbRMSE decreased by 3
0.037 m3/m3 and bias decreased by 0.03 m3/m3. The p-values indicated significant correlations 4
between the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and in situ measurements. Additionally, the overall 5
RMSE ranges of the downscaled SMAP validated by either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ data meet the criteria 6
for retrieval accuracy that RMSE < 0.04 m3/m3. Based on these results, we believe the 7
downscaling approach applied to SMAP soil moisture data is reliable and accurate for the 8
conditions evaluated and expect to implement the algorithm for providing a daily high spatial 9
resolution soil moisture product to the Contiguous United States. 10
With respect to these issues, future studies might include: (1) Other methodologies or 11
data sets that could be used to improve the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 correlation. Also, other land surface variables, 12
such as evapotranspiration (ET) and soil evaporative efficiency could be considered. (2) 13
Calibrated hydrological models could be helpful to provide correction for the SMAP soil 14
moisture retrievals (Sridhar et al., 2013). (3) Confidence in the soil moisture validation results 15
could be increased by having more in situ soil moisture stations within each soil moisture 16
retrieval grid for better representation of the spatial heterogeneity of the soil moisture. 17
18
24
FIGURES AND TABLES 1
2
Table 1. R2 of NLDAS soil moisture of top layer (m3/m3) at 6:00 a.m. versus daily surface skin temperature 3 (K) difference (1:30 p.m. - 1:30 a.m.) corresponding to NDVI classes from 0-1 in August for the three 4 SMAPVEX15 sampling sites: Walnut Gulch, Empire Ranch and Santa Rita. 5
Site NDVI Class R2 Slope
Walnut Gulch
0-0.1 0.528 -78.143
0.1-0.2 0.517 -77.023
0.2-0.3 0.5 -66.565
0.3-0.4 0.574 -78.334
> 0.4 0.809 -106.127
Empire Ranch
0-0.1 0.348 -53.090
0.1-0.2 0.294 -47.302
0.2-0.3 0.62 -66.239
0.3-0.4 0.47 -54.967
> 0.4 0.499 -61.209
Santa Rita
0-0.1 0.504 -79.861
0.1-0.2 0.366 -66.478
0.2-0.3 0.594 -75.577
0.3-0.4 0.638 -76.962
> 0.4 0.572 -79.173 6
25
Table 2. Statistical variables of validating (with upscaled PALS soil moisture) downscaled 1 km and 1 original 9 km SMAP soil moisture of descending overpass (6:00 a.m.) from five sampling days in August 2 2015 (The * symbol denotes p-value < |0.001|). 3
4 5
Date SM Dataset
Number of
Points R2 Slope µbRMSE
(m3/m3) Bias
(m3/m3) p-value
08/08 1 km 4477 0.697 1.552 0.02 0.002 *
9 km 70 0.597 1.915 0.022 0.004 0.259
08/10 1 km 4514 0.544 1.279 0.009 0.004 *
9 km 70 0.538 1.514 0.011 0.001 0.933
08/13 1 km 4544 0.429 1.128 0.011 0.01 0.003
9 km 69 0.209 1.006 0.018 0.018 0.024
08/16 1 km 4586 0.438 1.517 0.01 -0.002 *
9 km 70 0.103 0.854 0.003 0.003 0.713
08/18 1 km 4523 0.189 0.518 0.009 -0.001 *
9 km 70 0.003 0.07 0.013 0.007 0.106
26
Table 3. Statistical variables of validating (with in situ data) downscaled 1 km and original 9 km SMAP 1 soil moisture of descending overpass (6:00 a.m.) from five sampling days in August 2015. The validation 2 soil moisture data set is acquired from SMAPVEX15 in situ soil moisture sites (The * symbol denotes < 3 |0.001|). 4
5 6
Date SM Dataset
Number of
Points R2 Slope µbRMSE
(m3/m3) Bias
(m3/m3) p-value
08/08 1 km 48 0.409 0.236 0.044 -0.029 *
9 km 11 0.088 -0.126 0.088 -0.079 0.375
08/10 1 km 39 0.255 0.27 0.032 -0.023 0.001
9 km 11 * 0.004 0.081 -0.068 0.979
08/13 1 km 42 0.454 0.419 0.013 * *
9 km 11 0.353 -0.217 0.06 -0.035 0.054
08/16 1 km 44 0.443 0.352 0.02 -0.009 *
9 km 11 0.091 0.044 0.04 -0.024 0.368
08/18 1 km 39 0.733 0.705 0.006 -0.002 *
9 km 11 0.131 0.132 0.03 -0.023 0.274
27
1
2
Figure 1. Location of the study sites: (1) Walnut Gulch; (2) Empire Ranch and Santa Rita. Permanent in 3 situ soil moisture stations from the three study sites are denoted in red dots. 4
5
28
1
Figure 2. 10 km GPM (IMERG) 3-day accumulated Level 3 precipitation (unit: mm) from August 7-18, 2 2015 at Arizona (top row) and SMAPVEX15 (bottom row). 3 4
29
1 2 Figure 3. NLDAS surface soil moisture (m3/m3) at 6:00 a.m. versus daily surface skin temperature (K) 3 difference (1:30 p.m. - 1:30 a.m.) in August for the three SMAPVEX15 sampling sites: Walnut Gulch, 4 Empire Ranch and Santa Rita. The 𝜃𝜃 − ∆𝑇𝑇𝑠𝑠 point pairs are classified into 5 classes, based on the MODIS 5 NDVI value corresponding to each NLDAS grid. 6
7
30
1 2 Figure 4. SMAP Level 3 radiometer soil moisture (m3/m3) retrievals of 1 km downscaled, 9 km, 36 km, 3 and difference between 1 km and 9 km of descending overpasses (6:00 a.m.) in Arizona of the five 4 SMAPVEX15 sampling days. 5 6
31
1 2 Figure 5. 1 km downscaled SMAP soil moisture vs. 1 km upscaled PALS soil moisture and 9 km original 3 SMAP soil moisture retrievals of descending overpasses (6:00 a.m.) at SMAPVEX15 field (center 4 coordinates: 31.71oN, 110.68oW), from the five SMAPVEX15 sampling days. Boundaries of the Upper 5 San Pedro River Basin and San Pedro River are depicted in black and blue lines. The black grids outline 6 the 9 km grid boundaries. 7
8
32
1 2 Figure 6. Uncorrected 1 km soil moisture calculated from downscaling model comparing with 9 km 3 SMAP soil moisture of descending overpasses (6:00 a.m.) from the five SMAPVEX15 sampling days. 4 5
33
1 Figure 7. Soil moistures for 1 km downscaled SMAP, 1 km upscaled PALS and 9 km original SMAP soil 2 moistures of descending overpasses (6:00 a.m.) in SMAPVEX15 field from the five sampling days. 3
4
34
1
Figure 8. The empirical cumulative distribution function 𝑓𝑓(θ) of the 1 km downscaled SMAP, 1 km 2 upscaled PALS and 9 km original SMAP of descending overpasses (6:00 a.m.) for the five SMAPVEX15 3 sampling days. 4
5
35
1 2 Figure 9. Time series of the overall mean and standard deviation values of the 4 soil moisture data sets: 1 3 km downscaled SMAP, 1 km upscaled PALS and 9 km original SMAP of descending overpasses (6:00 4 a.m.) as well as in situ soil moisture measurements. 5
6
36
1
2 3 Figure 10. Validation scatterplots of 1 km downscaled and 9 km original SMAP soil moisture (m3/m3) 4 comparing with upscaled 1 km / 9 km PALS soil moisture (m3/m3). Warmer color in 1 km comparison plots 5 indicates higher density of scatter points. 6
7
37
1 2 Figure 11. Validation scatterplots of 1 km downscaled and 9 km SMAP soil moisture estimates (m3/m3) at 3 6:00 a.m. overpasses comparing with in situ soil moisture measurements for the five SMAPVEX15 4 sampling days. Comparison was made when there was a minimum of 8 in situ observations in each 1 km / 5 9 km SMAP soil moisture grid. 6
7
38
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